查询词典 nonlinear equation

In the sense of Von Karman large displacement, the governing equation of nonlinear dynamic response of the clamped circular plates under impact of a mass is established by using the virtual displacement principle and Galerkin's method in this paper. The effect of coupling between the impact load and the displacement of. the circular plates is considered. The governing equation is solved by applying the time increment method and the singular perturbation theory, and the asymptotic solutions of nonlinear dyna...

本文在Von Kármán大位移的意义上，利用虚位移原理伽辽金方法建立了圆板在物体撞击下的非线性动力响应的控制微分方程，在研究响应问题时，考虑了冲击载荷与圆板位移响应之间的耦合影响，文中使用时间增量法和奇异摄动理论求解问题的控制方程，获得了固支圆板非线性动力响应的近似解，并且求解了具体算例，绘出了圆板位移、应力响应曲线以及冲击力随时间的变化曲线。

Nonlinear Schrdinger equation of optical field in logarithmically saturable nonlinear media is derived firstly from scalar Helmholtz equation.

0引言近年来，光学孤子由于其独特的物理特性和广阔的应用前景，在光学领域引起了极大的关注[1~3]。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

In order to study the primary resonance and primary parametric resonance of a rectangular deck plate subject to harmonic disturbances in temperature field, by applying elastic theory, a nonlinear dynamical equation in partial differential form for the plate is established first. Then the nonlinear vibration equation in ordinary differential form is obtained based on Galerkin's method.

为了研究温度场中桥面矩形薄板受简谐激励的主共振－主参数共振问题，应用弹性力学理论建立其动力学方程，应用Galerkin方法将其转化为非线性振动方程。

The first part of this paper goes to a thoroughreview of studies on methods for nonlinear least squares problems, which are then,from the perspective of arithmetic design, classified into five major types: methodsbased on quasi-Newton equation, hybrid methods, factorized quasi-Newton method,trust-region methods, and self-scaling method. The second part of this paper turns thefocus toward a type of new algorithms for nonlinear least squares problems based onnew quasi-Newton equation.

本文的前半部分通过对非线性最小二乘各种求解方法的回顾，从算法设计的角度将求解方法划分为五大类：基于拟牛顿修正的方法，混合法，分解拟牛顿法，信赖域算法以及具有乘积结构类算法，本文后半部分给出了基于新拟牛顿方程的一类求解非线性最小二乘的新算法。

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

In this paper, we invert the condition equation into a complete nonlinear partial differential equation, and study some properties of the solution of this equation from a theoretical point.

本文把其条件方程转化为一个非线性偏微分方程，从理论角度探讨了一下此方程的解的一些性质。

Many natural phenomena and physical laws can be described by time dependent nonlinear differential equations, such as heat conduction equation, sound wave and elastic wave equation, reaction diffusion and convection diffusion equation, fluid and aerodynamics equations, etc.

大多数的自然现象与物理规律都可归结为与时间相关的非线性偏微分方程，诸如热传导方程、声波与弹性波方程、反应扩散与对流扩散方程、流体与气体力学方程组等发展方程。

In chapter 3, homogeneous balance method is used to deal with some problems of finding solutions of higher dimensional nonlinear evolution equation . By improving some key procedure of the method, the original equation is reduced to a linear equation , hence a great number of exact solutions for this are obtained.

第三章利用齐次平衡法研究了一些高维非线性演化方程和方程组的求解问题，通过对该方法的某些关键步骤的处理，将原方程转化为一线性的微分方程，从而获得了这些方程大量的多种精确解。

In chapter 3,we study the Zakharov-Kuznetsov-Modified Equal-Width equation by employing the extended Jacobi elliptic function expansion method and obtain some new solutions of Jacobi elliptic function type of the ZK-MEW equation.;Secondly,using sn-cn method,we study K(m,n,1) equation and obtained some new exact solutions when k=s=3,especially obtained abundand solitary solutions and trigonometric function solutions when m→0 and m→1;In chapter 4,Painleve singular analysis was applied to nonlinear PDE with variable coefficients.

第四章将Painleve奇性分析方法应用到带阻尼项的变系数Burgers方程中，并得到了该类Burgers方程具有Painleve性质的条件，给出了该类Burgers方程的Backlund变换，用所得Backlund变换得到了若干精确孤立波解，包括奇异孤立波解，这些解不等同于行波型孤立波解；用齐次平衡法得到了对数型DBM方程的Backlund变换，并获得了DBM方程的各种孤立波解，包括尖峰孤立波解和奇异尖峰孤立波解。

Vishnu entered a dark fourth dimensional dream that did not support his field or continued life.

毗瑟挐进入了一个第四密度的黑暗梦想，那里并不支持他的能量场或继续生命。

Leaders and decision-making persons use it to collect the data, including the information of unit work, handing in fee, oweing fee, prepaying fee,changing and afterpaying and account transfering of joining-insurance employee, and account paying of all kinds of insurances from hospitalization insurance institutions.The collected data is picked up, organized, switched and showed to user.

该子系统主要面向各级领导、决策分析人员；从各个医疗保险经办机构和定点医疗机构采集数据，包括在各个医疗保险经办机构处理的单位办公信息，单位缴费、欠费、预缴费信息，参保职工变更信息，参保职工增减变动信息，参保职工补缴信息，参保职工帐户划拨信息：包括各定点医疗机构处理的各险种帐户支出信息，各险种的统筹金支付信息等；将采集的数据提取，组织和转换，然后展示给用户。